Tessa's mother, Robyn Watts, said her daughter and son-in-law were in good spirits and preparing to return home.
"They seem to be doing quite well," she told ABC Radio.
"They were lucky in that they were in their cabin when it happened - unlike a lot of passengers who were dining - so at least they had access to their coats and were able to be warm.
"And they were in one of the last few lifeboats to actually get away from the ship." Ms Watts said the couple were expected to arrive in Sydney late on Monday.
"They were happy to be safe. It was a fairly confused atmosphere. I think they weren't really sure what was going on," she said.
"We were able to contact DFAT for them and the consulate met them when they got to the mainland, which was really helpful.
"They've been looked after quite well. They were given accommodation and clothes and they've sorted some airfares back for them." DFAT said consular officials were at the mainland reception point for all the evacuated Australian passengers, who were all given consular assistance.
They were trying to determine if any other Australians were on board.
-AAP